Counting Crows did a bunch of covers.
Round Here (1993) is a cover of Round Here by The Himalayans (1991)
The Ghost in You (1995) is a cover of The Ghost in You by The Psychedelic Furs (1984)
Big Yellow Taxi (2002) by Counting Crows feat. Vanessa Carlton is a cover of Big Yellow Taxi by Joni Mitchell (1970)
Blues Run the Game (2002) is a cover of Blues Run the Game by Jackson C. Frank (1965)
Friend of the Devil (2003) is a cover of Friend of the Devil by Grateful Dead (1970)
And a whole album of covers called Underwater Sunshine (Or What We Did On Our Summer Vacation)
Amie (2012) is a cover of Amie by Pure Prairie League (1972)
Ooh La La (2012) is a cover of Ooh La La by Faces (1973)
All My Failures (2012) is a cover of All My Failures by Dawes (2011)
The Ballad of El Goodo (2012) is a cover of The Ballad of El Goodo by Big Star (1972)
You Ain't Goin' Nowhere (2012) is a cover of You Ain't Goin' Nowhere by Bob Dylan and The Band (1975)
Untitled (Love Song) (2012) is a cover of Untitled (Love Song) by The Romany Rye (2009)
Start Again (2012) is a cover of Start Again by Teenage Fanclub (1997)
Coming Around (2012) is a cover of Coming Around by Travis (1999)
Meet on the Ledge (2012) is a cover of Meet on the Ledge by Fairport Convention (1968)